Boiling on a straight pin fin with variable thermal conductivity

This work theoretically investigated the thermal performance and stability characteristics of a straight pin fin subject to boiling considering a temperature-dependent thermal conductivity of fin, k=k _sat(1+b(T−T _sat)). Steady-state temperature distribution and the associated fin base heat flow were for the first time analytically found, whose stability characteristics were evaluated by linear stability analysis. A positive temperature coefficient b will raise both the fin's temperature and base heat flow. The corresponding stability for stable fin boiling was enhanced. A negative b results in an opposite trend. The use of a mean thermal conductivity in fin boiling calculations is discussed. Received on 3 November 1997     

Correlation equations for optimum design of annular fins with temperature dependent thermal conductivity

Correlation equations for optimum design of annular fins with temperature-dependent thermal conductivity are obtained in the present work. The nonlinear fin equation which is associated with variable thermal conductivity condition is solved by Adomian decomposition method that provides an analytical solution in the form of an infinite power series. The optimum radii ratio of an annular fin which maximizes the heat transfer rate has been found as a function of Biot number and the fin volume for a given thermal conductivity parameter describing the variation of the thermal conductivity. The fin volume is fixed to obtain the dimensionless geometrical parameters of the fin with maximum heat transfer rate. The data from the present solutions is correlated for a suitable range of Biot number and the fin volume. The simple correlation equations presented in this work can assist for thermal design engineers for optimum design of annular fins with temperature-dependent thermal conductivity.     

An analytical method for the optimum thermal design of convective longitudinal fin arrays

The paper analyzes the problem of the optimum thermal design of free and forced convection fin arrays composed of longitudinal fins with constant thickness. Two different optimization problems have been considered: the minimization of the weight for a given heat flow and the maximization of the heat flow for a given weight. Two different geometrical configurations of the fin array have been considered: closed array and open array. The procedure for the optimization is provided in a general case and a complete analytical solution of the problem, for the case with the tip approximated as being insulated, is developed. The paper contains several illustrative examples of the application of the proposed optimization procedure.     

Transient multiboiling in a pin fin with temperature dependent thermal conductivity

Transient heat conduction in fins undergoing different kinds of convective processes (film, transition, nucleated boiling and natural convection) as in multiboiling processes take place, is a strongly non-linear problem because of the abrupt changes in the heat transfer coefficient that occur at certain temperatures. Transient equations for the thermal fields and fluxes are solved simultaneously, giving the time constant of the process; the stationary solution is compared with the numerical or experimental values of other authors. Temperature dependencies of the heat transfer coefficient and the thermal conductivity is assumed due to the large interval of temperatures occurring. Network Simulation Method is used for the numerical solution, which gives simultaneously thermal field of temperatures and heat fluxes.     

Efficiency and optimisation of fin with temperature-dependent thermal conductivity: a simplified solution

An analytical simplified solution is proposed for temperature distribution and fin efficiency, when thermal conductivity is temperature dependent. An optimal linearization technique is used to solve the nonlinear equation. Based on classical solution, some accurate results are obtained and presented with thermal conductivity parameter and fin parameter. Arithmetic mean temperature is less precise than an equivalent thermal conductivity. Optimal thickness for rectangular fin is derived.     

Novel model of thermo-magneto-viscoelastic medium with variable thermal conductivity under effect of gravity

The basic equations for a homogeneous and isotropic thermo-magnetoviscoelastic medium are formulated based on three different theories, i.e., the GreenLindsay(G-L) theory, the coupled(CD) theory, and the Lord-Shulman(L-S) theory. The variable thermal conductivity is considered as a linear function of the temperature. Using suitable non-dimensional variables, these basic equations are solved via the eigenvalue approach. The medium is initially assumed to be stress-free and subject to a thermal shock.The numerical results reveal that the viscosity, the two-temperature parameter, the gravity term, and the magnetic field significantly influence the distribution of the physical quantities of the thermoelastic medium.     

Numerical study on a vertical plate with variable viscosity and thermal conductivity

Free convection over an isothermal vertical plate immersed in a fluid with variable viscosity and thermal conductivity is studied in this paper. We consider the two-dimensional, laminar and unsteady boundary layer equations. Using the appropriate variables, the basic governing equations are transformed to non-dimensional governing equations. These equations are then solved numerically using a very efficient implicit finite difference scheme known as Crank–Nicolson scheme. The fluid considered in this study is of viscous incompressible fluid of temperature dependent viscosity and thermal conductivity. The effect of varying viscosity and thermal conductivity on velocity, temperature, shear stress and heat transfer rate are discussed. The velocity and temperature profiles are compared with previously published works and are found to be in good agreement.     

Free convection effects on a vertical cone with variable viscosity and thermal conductivity

The present paper deals with a flow of a viscous incompressible fluid along a heated vertical cone, with due allowance for variations of viscosity and thermal diffusivity with temperature. The fluid viscosity is assumed to be an exponential function of temperature, and the thermal diffusivity is assumed to be a linear function of temperature. The governing equations for laminar free convection of the fluid are transformed into dimensionless partial differential equations, which are solved by a finite difference method with the Crank–Nicolson implicit scheme. Dependences of the flow parameters on the fluid viscosity and thermal conductivity are obtained.     

Flow of couple stress fluid with variable thermal conductivity

The steady flow and heat transfer of a couple stress fluid due to an inclined stretching cylinder are analyzed. The thermal conductivity is assumed to be temperature dependent. The governing equations for the flow and heat transfer are transformed into ordinary differential equations. Series solutions of the resulting problem are computed. The effects of various interested parameters, e.g., the couple stress parameter, the angle of inclination, the mixed convection parameter, the Prandtl number, the Reynolds number, the radiation parameter, and the variable thermal conductivity parameter, are illustrated. The skin friction coefficient and the local Nusselt number are computed and analyzed. It is observed that the heat transfer rate at the surface increases while the velocity and the shear stress decrease when the couple stress parameter and the Reynolds number increase. The temperature increases when the Reynolds number increases.     

Three-dimensional stretched flow of Jeffrey fluid with variable thermal conductivity and thermal radiation

This article addresses the three-dimensional stretched flow of the Jeffrey fluid with thermal radiation. The thermal conductivity of the fluid varies linearly with respect to temperature. Computations are performed for the velocity and temperature fields. Graphs for the velocity and temperature are plotted to examine the behaviors with different parameters. Numerical values of the local Nusselt number are presented and discussed. The present results are compared with the existing limiting solutions, showing good agreement with each other.     

Boundary layer flow and heat transfer past a stretching plate with variable thermal conductivity

In the present paper, the boundary layer flow of viscous incompressible fluid over a stretching plate has been considered to solve heat flow problem with variable thermal conductivity. First, using similarity transformation, the components of velocity have been obtained. Then, the heat flow problem has been considered in two ways: (i) prescribed surface temperature (PST), and (ii) prescribed stretching plate heat flux (PHF) in case of variable thermal conductivity. Due to variable thermal conductivity, temperature profile has its two part—one mean temperature and other temperature profile induced due to variable thermal conductivity. The related results have been discussed with the help of graphs.     

The optimum fin spacing of circular tube bank fin heat exchanger with vortex generators

In real application, once the pattern of fin is determined, fin spacing of tube bank fin heat exchanger can be adjusted in a small region, and air flow velocity in the front of the heat exchanger is not all the same. Therefore, the effects of fin spacing on heat transfer performance of such heat exchanger are needed. This paper numerically studied the optimal fin spacing regarding the different front flow velocities of a circular tube bank fin heat exchanger with vortex generators. To screen the optimal fin spacing, an appropriate evaluation criterion JF was used. The results show that when front velocity is 1.75 m/s, the optimal fin spacing is 2.25 mm, when front velocity is 2.5 m/s, the optimal fin spacing is 2 mm, and when front velocity is higher than 2.5 m/s, the optimal fin spacing is 1.75 mm.     

Performance analysis and optimization of radiating fins with a step change in thickness and variable thermal conductivity by homotopy perturbation method

Although tapered fins transfer more rate of heat per unit volume, they are not found in every practical application because of the difficulty in manufacturing and fabrications. Therefore, there is a scope to modify the geometry of a constant thickness fin in view of the less difficulty in manufacturing and fabrication as well as betterment of heat transfer rate per unit volume of the fin material. For the better utilization of fin material, it is proposed a modified geometry of new fin with a step change in thickness (SF) in the literature. In the present paper, the homotopy perturbation method has been used to evaluate the temperature distribution within the straight radiating fins with a step change in thickness and variable thermal conductivity. The temperature profile has an abrupt change in the temperature gradient where the step change in thickness occurs and thermal conductivity parameter describing the variation of thermal conductivity has an important role on the temperature profile and the heat transfer rate. The optimum geometry which maximizes the heat transfer rate for a given fin volume has been found. The derived condition of optimality gives an open choice to the designer.     

MHD flow and heat transfer over a stretching surface with variable thermal conductivity and partial slip

In this paper we analyze the flow and heat transfer of an MHD fluid over an impermeable stretching surface with variable thermal conductivity and non-uniform heat source/sink in the presence of partial slip. The governing partial differential equations of the problem are reduced to nonlinear ordinary differential equations by using a similarity transformation. The temperature boundary conditions are assumed to be linear functions of the distance from the origin. Analytical solutions of the energy equations for Prescribed Surface Temperature (PST) and Prescribed Heat Flux (PHF) cases are obtained in terms of a hypergeometric function, without applying the boundary-layer approximation. The effects of the governing parameters on the flow and heat transfer fields are presented through tables and graphs, and they are discussed. Furthermore, the obtained numerical results for the skin friction, wall-temperature gradient and wall temperature are analyzed and compared with the available results in the literature for special cases.     

Flow of variable thermal conductivity fluid due to inclined stretching cylinder with viscous dissipation and thermal radiation

The aim of the present study is to investigate the flow of the Casson fluid by an inclined stretching cylinder. A heat transfer analysis is carried out in the presence of thermal radiation and viscous dissipation effects. The temperature dependent thermal conductivity of the Casson fluid is considered. The relevant equations are first simplified under usual boundary layer assumptions, and then transformed into ordinary differential equations by suitable transformations. The transformed ordinary differential equations are computed for the series solutions of velocity and temperature. A convergence analysis is shown explicitly. Velocity and temperature fields are discussed for different physical parameters by graphs and numerical values. It is found that the velocity decreases with the increase in the angle of inclination while increases with the increase in the mixed convection parameter. The enhancement in the thermal conductivity and radiation effects corresponds to a higher fluid temperature. It is also found that heat transfer is more pronounced in a cylinder when it is compared with a flat plate. The thermal boundary layer thickness increases with the increase in the Eckert number. The radiation and variable thermal conductivity decreases the heat transfer rate at the surface.